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Nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-02-13 DOI: 10.1016/j.aml.2025.109498
Quanguo Zhang
{"title":"Nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms","authors":"Quanguo Zhang","doi":"10.1016/j.aml.2025.109498","DOIUrl":"10.1016/j.aml.2025.109498","url":null,"abstract":"<div><div>In this paper, we study the nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms. We give an answer to an open problem posed in D’Abbicco (2014). Moreover, comparing with the existing results, our results do not require any positivity condition of the initial values. The proof of our results is based on the asymptotic properties of solutions for an integral inequality.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109498"},"PeriodicalIF":2.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The inverse source problem for a fractional diffusion-wave equation with inexact order: An asymptotically optimal strategy
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-02-07 DOI: 10.1016/j.aml.2025.109496
Dinh Nguyen Duy Hai
{"title":"The inverse source problem for a fractional diffusion-wave equation with inexact order: An asymptotically optimal strategy","authors":"Dinh Nguyen Duy Hai","doi":"10.1016/j.aml.2025.109496","DOIUrl":"10.1016/j.aml.2025.109496","url":null,"abstract":"<div><div>Inverse source problems frequently occur in real-world applications, such as pinpointing the location of contaminant sources in areas that are difficult to access. In this paper, we consider an inverse source problem of identifying an unknown source term in an abstract fractional diffusion-wave equation with inexact order. Due to the ill-posed nature of the problem, we propose a truncation method to achieve a stable solution. Under a Hölder-type source condition, we establish an asymptotically optimal convergence estimate by utilizing measurements of both the derivative order and the final time.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109496"},"PeriodicalIF":2.9,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symplectic mixed spectral element time domain method for 3-D Schrödinger–Maxwell equations under Lorenz gauge
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-02-07 DOI: 10.1016/j.aml.2025.109497
Chengzhuo Zhao, Wenjie Tang, Kangshuai Du, Na Liu
{"title":"Symplectic mixed spectral element time domain method for 3-D Schrödinger–Maxwell equations under Lorenz gauge","authors":"Chengzhuo Zhao,&nbsp;Wenjie Tang,&nbsp;Kangshuai Du,&nbsp;Na Liu","doi":"10.1016/j.aml.2025.109497","DOIUrl":"10.1016/j.aml.2025.109497","url":null,"abstract":"<div><div>In this work, Hamiltonian variational principle is employed to prove that Schrödinger–Maxwell (SM) equations under Lorenz gauge exhibit a symplectic structure. Based on this, symplectic mixed spectral element time domain method (<span><math><mtext>S-MSETD</mtext></math></span>) for SM equations under Lorenz gauge is proposed. This method is a structure-preserving geometric algorithm that achieves high accuracy, particularly in long-term simulation. Simultaneously, to address the incompatibility issue between the divergence operator acting on the magnetic vector potential <span><math><mi>A</mi></math></span> and the edge spectral element method (SEM), an auxiliary variable <span><math><mrow><mi>p</mi><mo>=</mo><mo>∇</mo><mi>⋅</mi><mi>A</mi></mrow></math></span> is introduced. This adjustment allows SM equations under Lorenz gauge to be effectively discretized using mixed SEM (MSEM). Finally, the effectiveness of S-MSETD is validated through numerical simulations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109497"},"PeriodicalIF":2.9,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coupled five-point lattices: Lax pairs and Hamiltonian structures
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-02-06 DOI: 10.1016/j.aml.2025.109484
Minxin Jia, Xianguo Geng
{"title":"Coupled five-point lattices: Lax pairs and Hamiltonian structures","authors":"Minxin Jia,&nbsp;Xianguo Geng","doi":"10.1016/j.aml.2025.109484","DOIUrl":"10.1016/j.aml.2025.109484","url":null,"abstract":"<div><div>A hierarchy of lattice equations, including a coupled five-point lattice equation, is proposed. By employing the zero-curvature equation, Lax pairs for this hierarchy are derived from a 4 × 4 linear matrix spectral problem. Subsequently, the Hamiltonian structure of the hierarchy is established using the trace identity. Furthermore, infinitely many conservation laws for the coupled five-point lattice equation are presented.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109484"},"PeriodicalIF":2.9,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A comparative study of dynamic models for gravity-driven particle-laden flows
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-02-05 DOI: 10.1016/j.aml.2025.109480
Wing Pok Lee , Jonathan D. Woo , Luke F. Triplett , Yifan Gu , Sarah C. Burnett , Lingyun Ding , Andrea L. Bertozzi
{"title":"A comparative study of dynamic models for gravity-driven particle-laden flows","authors":"Wing Pok Lee ,&nbsp;Jonathan D. Woo ,&nbsp;Luke F. Triplett ,&nbsp;Yifan Gu ,&nbsp;Sarah C. Burnett ,&nbsp;Lingyun Ding ,&nbsp;Andrea L. Bertozzi","doi":"10.1016/j.aml.2025.109480","DOIUrl":"10.1016/j.aml.2025.109480","url":null,"abstract":"<div><div>The dynamics of viscous thin-film particle-laden flows down inclined surfaces are commonly modeled with one of two approaches: a diffusive flux model or a suspension balance model. The diffusive flux model assumes that the particles migrate via a diffusive flux induced by gradients in both the particle concentration and the effective suspension viscosity. The suspension balance model introduces non-Newtonian bulk stress with shear-induced normal stresses, the gradients of which cause particle migration. Both models have appeared in the literature of particle-laden flow with virtually no comparison between the two models. For particle-laden viscous flow on an incline, in a thin-film geometry, one can use lubrication theory to derive a compact dynamic model in the form of a 2 × 2 system of conservation laws. We can then directly compare the two theories side by side by looking at similarities and differences in the flux functions for the conservation laws, and in exact and numerical simulations of the equations. We compare the flux profiles over a range of parameters, showing fairly good agreement between the models, with the biggest difference involving the behavior at the free surface. We also consider less dense suspensions at lower inclination angles where the dynamics involve two shock waves that can be clearly measured in experiments. In this context the solutions differ by no more than about 10%, suggesting that either model could be used for this configuration.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109480"},"PeriodicalIF":2.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143377632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A free boundary problem with impulsive harvesting in small advection environment
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-02-03 DOI: 10.1016/j.aml.2025.109482
Yanglei Li, Ningkui Sun
{"title":"A free boundary problem with impulsive harvesting in small advection environment","authors":"Yanglei Li,&nbsp;Ningkui Sun","doi":"10.1016/j.aml.2025.109482","DOIUrl":"10.1016/j.aml.2025.109482","url":null,"abstract":"<div><div>This paper is devoted to the study of the combined effects of impulsive harvesting and small advection on the dynamical behavior of solutions to a free boundary model. By introducing a one-parameter family of initial data <span><math><mrow><mi>σ</mi><mi>ϕ</mi></mrow></math></span> with <span><math><mrow><mi>σ</mi><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mi>ϕ</mi></math></span> being a compactly supported function, under some suitable assumptions, we obtain a threshold value <span><math><msup><mrow><mi>σ</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> such that spreading happens when <span><math><mrow><mi>σ</mi><mo>&gt;</mo><msup><mrow><mi>σ</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>, vanishing happens when <span><math><mrow><mi>σ</mi><mo>≤</mo><msup><mrow><mi>σ</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109482"},"PeriodicalIF":2.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A blowup criterion for the three-dimensional compressible viscous micropolar fluids
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-02-03 DOI: 10.1016/j.aml.2025.109483
Meiyun Dai , Jinxia Liu , Yinghui Zhang
{"title":"A blowup criterion for the three-dimensional compressible viscous micropolar fluids","authors":"Meiyun Dai ,&nbsp;Jinxia Liu ,&nbsp;Yinghui Zhang","doi":"10.1016/j.aml.2025.109483","DOIUrl":"10.1016/j.aml.2025.109483","url":null,"abstract":"<div><div>We give a new blowup criterion for the strong solution of Cauchy problem for three-dimensional micropolar fluid equations with vacuum. It shows that the strong or smooth solution exists globally if the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>:</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>-norm of the density is bounded, where <span><math><mi>q</mi></math></span> is a positive constant. Particularly, we succeed in removing the technical condition <span><math><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></mrow></math></span> in Hou and Xu (2024).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109483"},"PeriodicalIF":2.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A kernel function based regularized method for boundary value problems with noisy information
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-02-01 DOI: 10.1016/j.aml.2025.109481
X.L. Li , F.Z. Geng , Y.Q. Gao
{"title":"A kernel function based regularized method for boundary value problems with noisy information","authors":"X.L. Li ,&nbsp;F.Z. Geng ,&nbsp;Y.Q. Gao","doi":"10.1016/j.aml.2025.109481","DOIUrl":"10.1016/j.aml.2025.109481","url":null,"abstract":"<div><div>Taking advantage of the reproducing kernel theory, several effective numerical algorithms have been developed to solve boundary value problems (BVPs) with the exact right side functions. However, these methods have difficulty in solving effectively linear boundary value problems when the right side of the equation has contaminated data. The objective of this letter is to introduce a robust numerical algorithm for linear BVPs with noisy right-hand side functions information. To overcome the challenges of the noisy right-hand side functions, the idea of regularization is used. Numerical simulation is employed to illustrate the superiority of the present method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109481"},"PeriodicalIF":2.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A monotone block coordinate descent method for solving absolute value equations
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-01-30 DOI: 10.1016/j.aml.2025.109479
Tingting Luo , Jiayu Liu , Cairong Chen , Qun Wang
{"title":"A monotone block coordinate descent method for solving absolute value equations","authors":"Tingting Luo ,&nbsp;Jiayu Liu ,&nbsp;Cairong Chen ,&nbsp;Qun Wang","doi":"10.1016/j.aml.2025.109479","DOIUrl":"10.1016/j.aml.2025.109479","url":null,"abstract":"<div><div>In Noor et al. (2011), the second-order Taylor expansion of the objective function is incorrectly used in constructing the descent direction. Thus, the proposed block coordinate descent method is non-monotone and a strict convergence analysis is lack. This motivates us to propose a monotone block coordinate descent method for solving absolute value equations. Under appropriate conditions, we analyze the global convergence of the algorithm and conduct numerical experiments to demonstrate its feasibility and effectiveness.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109479"},"PeriodicalIF":2.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite element method for the coupled Stokes–Darcy–Darcy system
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-01-29 DOI: 10.1016/j.aml.2025.109477
Liyun Zuo , Guangzhi Du
{"title":"Finite element method for the coupled Stokes–Darcy–Darcy system","authors":"Liyun Zuo ,&nbsp;Guangzhi Du","doi":"10.1016/j.aml.2025.109477","DOIUrl":"10.1016/j.aml.2025.109477","url":null,"abstract":"<div><div>In this article, we propose and analyze the finite element method for the mixed Stokes–Darcy–Darcy system which involves free flow in conduits coupled with confined flow in fractured porous media. The interactions on the interfaces come from the classical Stokes–Darcy system and the famous bulk-fracture system. Rigorously theoretical results are derived and some numerical results are provided to verify the theoretical findings.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109477"},"PeriodicalIF":2.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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